A) \[^{10}{{C}_{4}}\]
B) \[{{-}^{10}}{{C}_{4}}\]
C) \[^{10}{{C}_{5}}\]
D) \[^{10}{{C}_{6}}\]
Correct Answer: C
Solution :
\[\because \]\[n=10\]is even \[\therefore \]Middle term in the expansion of \[{{\left( x+\frac{1}{x} \right)}^{10}}\]is \[\left( \frac{10}{2}+1 \right)\]th term = 6th term \[\therefore \] \[{{T}_{6}}{{=}^{10}}{{C}_{5}}{{x}^{5}}{{\left( \frac{1}{x} \right)}^{5}}\] \[{{=}^{10}}{{C}_{5}}\] Hence, coefficient of the middle term is\[^{10}{{C}_{5}}\].
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